Problem: What do the following two equations represent? $-x-3y = -1$ $-x-3y = 2$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-x-3y = -1$ $-3y = x-1$ $y = -\dfrac{1}{3}x + \dfrac{1}{3}$ Putting the second equation in $y = mx + b$ form gives: $-x-3y = 2$ $-3y = x+2$ $y = -\dfrac{1}{3}x - \dfrac{2}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.